Recent progress in the determination of hadronic matrix elements has revealed a tension between the measured value of epsilon’/epsilon, which quantifies direct CP-violation in K to pi pi decays, and the Standard-Model (SM) prediction. On the other hand, the standard analytic solution of the next-to-leading order (NLO) renormalization group (RG) evolution for the DeltaS = 1 Wilson coefficients suffers from several singularities. In the first part of this talk, we will introduce a singularity-free analytic solution of the RG evolution, and give a new prediction value of the epsilon’/epsilon in the SM at the NLO, which also implies the epsilon’ discrepancy. In the second part, we will show that it is possible to cure the epsilon’ discrepancy in the Minimal Supersymmetric Standard Model with squark masses above 3 TeV without overshooting epsilon. This solution exploits two features of supersymmetry, the possibility of large isospin-breaking contributions (enhancing epsilon’) and the Majorana nature of gluinos (permitting a suppression of epsilon). Our solution involves no fine-tuning of CP phases or other parameters.
This talk is based on
arXiv:1604.07400 and
arXiv:1607.06727.